Empty canisters which contained nitrous oxide have been found at various locations in the Alton area.
A Hampshire Constabulary spokeswoman said: “I can confirm that we received a report at 1pm on July 4 of about 20 aluminium bottles, two inches long, outside All Saints’ Church Hall, Queens Road, Alton.
“The informant advised that she had disposed of them. The informant was advised to call 101 again if this becomes a regular occurrence.”
Other members of the public said on Facebook that they had seen them outside a shop in Alton and on a public grassy area in East Worldham, although these findings were not reported to the police.
Nitrous oxide - commonly known as laughing gas - is used medically, in combination with other medications for anaesthesia in dentistry, and with at least 21 per cent oxygen as pain relief for women in labour.
It is used in the catering industry to make whipped cream.
But the gas in these canisters is also thought to be inhaled as a recreational drug.
Anyone finding such canisters should report their location to the police on 101.